Models of Three‐dimensional Flux Ropes

A crucial problem in the study of coronal mass ejections is understanding the evolution prior to the eruption and the development of initial configurations and boundary conditions that can produce an eruption of the field configuration and the identification of observable features from these configurations. In this paper we present a general framework to derive approximate equilibrium configurations suitable to describe pre-eruption states, using an approach originally developed for the Earth's magnetotail but including magnetic shear and gravity. The solutions hold for configurations that vary most strongly in one spatial direction perpendicular to the direction of gravity. We illustrate the approach by deriving configurations for both force-free and non-force-free states. The variable models contain a twisted flux rope connected to the photosphere and anchored in the corona by an overlying arcade. The models may also include a magnetic configuration above the flux rope typical for helmet streamers.